Prime factorization of $$$2505$$$

Find the prime factorization of $$$2505$$$.

Start with the number $$$2$$$.

Determine whether $$$2505$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$2505$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2505$$$ by $$${\color{green}3}$$$: $$$\frac{2505}{3} = {\color{red}835}$$$.

Determine whether $$$835$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$835$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$835$$$ by $$${\color{green}5}$$$: $$$\frac{835}{5} = {\color{red}167}$$$.

The prime number $$${\color{green}167}$$$ has no other factors then $$$1$$$ and $$${\color{green}167}$$$: $$$\frac{167}{167} = {\color{red}1}$$$.

Since we have obtained $$$1$$$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$2505 = 3 \cdot 5 \cdot 167$$$.

The prime factorization is $$$2505 = 3 \cdot 5 \cdot 167$$$A.